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Predicting Damage Evolution in Composites with Explicit Representation of Discrete Damage Modes

Living reference work entry

Abstract

Polymer matrix composites (PMCs) are playing rapidly increasing roles in future military and civilian industries. Damage tolerance analysis is an integral part of PMC structural design. Considerable research efforts have been invested to establish predictive capabilities, but thus far high-fidelity strength and durability prediction capabilities are yet to be established. Advanced numerical methods that can explicitly resolve the multiple-damage processes and their nonlinear coupling at various scales are highly desired. This paper first reviews the recent development of advanced numerical methods, including eXtended Finite Element Method (X-FEM), phantom node methods (PNM), and the Augmented Finite Element Method (A-FEM), in handling the multiple-damage coupling in composites. The capability of these methods in representing various composite damage modes explicitly with embedded nonlinear fracture models (such as cohesive zone models) makes them excellent candidates for high-fidelity failure analyses of composites. The detailed formulation of A-FEM and its implementation to a popular commercial software package (ABAQUS) as a user-defined element has been given. Successful simulations of composites at various scales using the framework of A-FEM are presented and the numerical and material issues associated with these high-fidelity analyses are discussed. Through the numerical predictions and the direct comparisons to experimental results, it has been demonstrated that high-fidelity failure analyses can be achieved with the A-FEM through careful calibration of nonlinear material properties and cohesive fracture parameters and with proper considerations of the different length scales within which these damage processes operate.

Keywords

Linear Elastic Fracture Mechanic Cohesive Zone Fracture Process Zone Transverse Crack Cohesive Zone Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. D.F. Adams, T.R. King, D.M. Blackketter, Evaluation of the transverse flexure test method for composite materials. Compos. Sci. Technol. 39, 341–353 (1990)CrossRefGoogle Scholar
  2. G. Bao et al., The role of material orthotropy in fracture specimens for composites. Int. J. Sol. Struct. 29, 1105–1116 (1992)CrossRefMATHGoogle Scholar
  3. G.I. Barenblatt, The formation of equilibrium cracks during brittle fracture: general ideas and hypotheses, axially symmetric cracks. Appl. Math. Mech. 23, 622–636 (1959)CrossRefMATHMathSciNetGoogle Scholar
  4. G.I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, in Advances in Applied Mechanics, ed. by H.L. Dryden, T. Von Karman (Academic, New York, 1962), pp. 55–129Google Scholar
  5. Z.P. Bazant, J. Planas, Fracture and Size Effect in Concrete and Other Quasibrittle Materials (CRC Press, Boca Raton, 1998)Google Scholar
  6. P.P. Camanho, C.G. Davila, M.F. De Moura, Numerical simulation of mixed-mode progressive delamination in composite materials. J. Compos. Mater. 37, 1415–1438 (2003)CrossRefGoogle Scholar
  7. P.P. Camanho et al., Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear. Compos. Part A Appl. Sci. Manuf. 37, 165–176 (2006)CrossRefGoogle Scholar
  8. A. Carpinteri, G. Colombo, Numerical analysis of catastrophic softening behaviour(snap-back instability). Comput. Struct. 31, 607–636 (1989)CrossRefGoogle Scholar
  9. A. Carpinteri, G. Ferro, Fracture assessment in concrete structures, in Concrete Structure Integrity, ed. by I. Milne, R.O. Ritchie, B. Karihaloo (Elsevier Science, Amsterdam, 2003)Google Scholar
  10. S.W. Case, K.L. Reifsnider, MRLife 12 Theory Manual – Composite Materials (Materials Response Group, Virginia Polytechnical Institute and State University, Blacksburg, 1999)Google Scholar
  11. J.L. Chaboche, P.M. Lesne, J.F. Maire, Continuum damage mechanics, anisotropy and damage deactivation for brittle materials like concrete and ceramic composites. Int. J. Damage Mech. 4(1), 5–22 (1995)CrossRefGoogle Scholar
  12. J.L. Chaboche, R. Girard, P. Levasseur, On the interface debonding models. Int. J. Damage Mech. 6, 220–256 (1997)CrossRefGoogle Scholar
  13. K.Y. Chang, S. Liu, F.K. Chang, Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings. J. Compos. Mater. 25, 274–301 (1991)Google Scholar
  14. H.Y. Choi, F.K. Chang, A model for predicting damage in graphite/epoxy laminated composites resulting from low-velocity point impact. J. Compos. Mater. 26, 2134–2169 (1992)CrossRefGoogle Scholar
  15. G. Clark, Modeling of impact damage in composite laminates. Composites 20, 209–214 (1989)CrossRefGoogle Scholar
  16. A. Corigliano, Formulation, identification and use of interface models in the numerical analysis of composite delamination. Int. J. Sol. Struct. 30, 2779–2811 (1993)CrossRefMATHGoogle Scholar
  17. B.N. Cox, Q.D. Yang, In quest of virtual tests for structural composites. Science 314, 1102–1107 (2006)CrossRefGoogle Scholar
  18. W.C. Cui, M.R. Wisnom, N. Jones, Failure mechanisms in three and four point short beam bending tests of unidirectional glass/epoxy. J. Strain. Anal. 27(4), 235–243 (1992)CrossRefGoogle Scholar
  19. C.G. Davila, P.P. Camanho, C.A. Rose, Failure criteria for FPR laminates. J. Compos. Mater. 39, 323–345 (2005)CrossRefGoogle Scholar
  20. R. de Borst, Numerical aspects of cohesive-zone models. Eng. Fract. Mech. 70, 1743–1757 (2003)CrossRefGoogle Scholar
  21. R. de Borst et al., On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials. Comput. Mech. 17(1–2), 130–141 (1995)CrossRefMATHGoogle Scholar
  22. R. de Borst, J.J.C. Remmers, A. Needleman, Mesh-independent discrete numerical representations of cohesive-zone models. Eng. Fract. Mech. 73(2), 160–177 (2006)CrossRefGoogle Scholar
  23. J. Dowlbow, M. A. Kahaleel, J. Mitchell, Multiscale Mathematics Initiative: A Roadmap. A Report to Department of Energy Report PNNL-14966 (2004)Google Scholar
  24. D.S. Dugdale, Yielding of steel sheets containing slits. J. Mech. Phys. Sol. 8, 100–104 (1960)CrossRefGoogle Scholar
  25. G.J. Dvorak, N. Laws, Analysis of progressive matrix cracking in composite laminates. II. First ply failure. J. Compos. Mater. 21, 309–329 (1987)CrossRefGoogle Scholar
  26. M. Elices et al., The cohesive zone model: advantages, limitations and challenges. Eng. Fract. Mech. 69, 137–163 (2002)CrossRefGoogle Scholar
  27. X.J. Fang, Q.D. Yang, B.N. Cox, An augmented cohesive zone element for arbitrary crack coalescence and bifurcation in heterogeneous materials. Int. J. Numer. Meth. Eng. 88, 841–861 (2010)CrossRefMathSciNetGoogle Scholar
  28. X.J. Fang et al., High-fidelity simulations of multiple fracture processes in a laminated composites in tension. J. Mech. Phys. Sol. 59, 1355–1373 (2011a)CrossRefMATHGoogle Scholar
  29. X.J. Fang et al., An augmented cohesive zone element for arbitrary crack coalescence and bifurcation in heterogeneous materials. Int. J. Numer. Meth. Eng. 88, 841–861 (2011b)CrossRefMATHGoogle Scholar
  30. A. Fawcett, J. Trostle, S. Ward, in International Conference on Composite Materials, Gold Coast, 1997Google Scholar
  31. S.F. Finn, Y.F. He, G.S. Springer, Delaminations in composite plates under transverse impact loads – experimental results. Compos. Struct. 23, 191–204 (1993)CrossRefGoogle Scholar
  32. J. Fish, A. Ghouali, Multiscale analysis sensitivity analysis for composite materials. Int. J. Numer. Meth. Eng. 50, 1501–1520 (2001)CrossRefMATHGoogle Scholar
  33. C. Gonzalez, J. LLorca, Multiscale modeling of fracture in fiber-reinforced composites. Acta Mater. 54, 4171–4181 (2006)CrossRefGoogle Scholar
  34. S. Goutianos, B.F. Sorensen, Path dependence of truss-like mixed mode cohesive laws. Eng. Fract. Mech. 91, 117–132 (2012)CrossRefGoogle Scholar
  35. S. Hallett, M.R. Wisnom, Numerical investigation of progressive damage and the effect of layup in notched tensile tests. J. Compos. Mater. 40, 1229–1245 (2006a)CrossRefGoogle Scholar
  36. S.R. Hallett, M.R. Wisnom, Experimental investigation of progressive damage and the effect of layup in notched tensile tests. J. Compos. Mater. 40, 119–141 (2006b)CrossRefGoogle Scholar
  37. A. Hansbo, P. Hansbo, A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput. Meth. Appl. Mech. Eng. 193, 3523–3540 (2004)CrossRefMATHMathSciNetGoogle Scholar
  38. M.-Y. He, J.W. Hutchinson, Crack deflection at an interface between dissimilar materials. Int. J. Sol. Struct. 25, 1053–1067 (1989)CrossRefGoogle Scholar
  39. A. Hillerborg, M. Modéer, P.E. Peterson, Analysis of crack propagation and crack growth in concrete by means of fracture mechanics and finite elements. Cement. Concr. Res. 6, 773–782 (1976)CrossRefGoogle Scholar
  40. E.V. Iarve, D. Mollenhauer, R. Kim, Theoretical and experimental investigation of stress redistribution in open-hole composite laminates due to damage accumulation. Compos. Part A 36, 163–171 (2005)CrossRefGoogle Scholar
  41. H.M. Inglis et al., Cohesive modeling of dewetting in particulate composites: micromechanics vs. multiscale finite element analysis. Mech. Mater. 39, 580–595 (2007)CrossRefGoogle Scholar
  42. P.M. Jelf, N.A. Fleck, The failure of composite tubes due to combined compression and torsion. J. Mater. Sci. Lett. 29, 3080 (1994)CrossRefGoogle Scholar
  43. A.S. Kaddorur, M.J. Hinton, P.D. Soden, A comparison of the predictive capabilities of current failure theories for composite laminates: additional contributions. Compos. Sci. Technol. 64, 449–476 (2004)CrossRefGoogle Scholar
  44. M.S. Kafkalidis et al., Deformation and fracture of an adhesive layer constrained by plastically-deforming adherends. Int. J. Adhes. Sci. Technol. 14, 1593–1646 (2000)CrossRefGoogle Scholar
  45. M. Kumosa, G. Odegard, Comparison of the +/−45 tensile and Iosipescu shear tests for woven fabric composites. J. Compos. Technol. Res. 24, 3–15 (2002)CrossRefGoogle Scholar
  46. P. Ladeveze, Multiscale modelling and computational strategies. Int. J. Numer. Meth. Eng. 60, 233–253 (2004)CrossRefMATHMathSciNetGoogle Scholar
  47. I. Lapczyk, J. Hurtado, Progressive damage modeling in fiber-reinforced materials. Compos. Part A 38, 2333–2341 (2007)CrossRefGoogle Scholar
  48. F. Laurin, N. Carrere et al., A multi-scale progressive failure approach for composite laminates based on thermodynamical viscoelastic and damage models. Compos. Part A 38, 198–209 (2007)CrossRefGoogle Scholar
  49. D.S. Ling, Q.D. Yang, B.N. Cox, An augmented finite element method for modeling arbitrary discontinuities in composite materials. Int. J. Fract. 156, 53–73 (2009)CrossRefMATHGoogle Scholar
  50. D.S. Ling et al., Nonlinear fracture analysis of delamination crack jumps in laminated composites. J. Aerosp. Eng. 24, 181–188 (2011)CrossRefGoogle Scholar
  51. J. LLorca, C. González, Multiscale modeling of composite materials: a roadmap towards virtual testing. Adv. Mater. 23, 5130–5147 (2011)CrossRefGoogle Scholar
  52. P. Maimi et al., A continuum damage model for composite laminates: Part I – Constitutive model. Mech. Mater. 39, 897–908 (2007)CrossRefGoogle Scholar
  53. A. Matzenmiller, J. Lubliner, R.L. Taylor, A constitutive model for anisotropic damage in fiber-composites. Mech. Mater. 20, 125–152 (1995)CrossRefGoogle Scholar
  54. L.N. McCartney, Physically based damage models for laminated composites. J. Mater. Des. Appl. 217(3), 163–199 (2003)Google Scholar
  55. J. Mergheim, E. Kuhl, P. Steinmann, A finite element method for the computational modeling of cohesive cracks. Int. J. Numer. Meth. Eng. 63, 276–289 (2005)CrossRefMATHGoogle Scholar
  56. N. Moës, T. Belytschko, Extended finite element method for cohesive crack growth. Eng. Fract. Mech. 69, 813–833 (2002)CrossRefGoogle Scholar
  57. N. Moes, J. Dolbow, T. Belytschko, Finite element method for crack growth without remeshing. Int. J. Numer. Meth. Eng. 46, 131–150 (1999)CrossRefMATHGoogle Scholar
  58. A. Needleman, An analysis of decohesion along an imperfect interface. Int. J. Fract. 42, 21–40 (1990)CrossRefGoogle Scholar
  59. T.K. O’Brien, S.A. Salpekar, Scale effects on the transverse tensile strength of carbon/epoxy composites. Compos. Mater. Test. Des. 11(ASTM STP 1206), 23–52 (1993)Google Scholar
  60. T.K. O'Brien et al., Influence of specimen configuration and size on composite transverse tensile strength and scatter measured through flexure testing. J. Compos. Technol. Res. 25, 50–68 (2003)Google Scholar
  61. J.T. Oden, K. Vemaganti, N. Moes, Hierarchical modeling of heterogeneous solids. Comput. Method. Appl. Mech. Eng. 172, 3–25 (1999)CrossRefMATHMathSciNetGoogle Scholar
  62. J.T. Oden et al., Simulation-Based Engineering Science – Revolutionizing Engineering Science through Simulation (NSF, 2006)Google Scholar
  63. C. Oskay, J. Fish, Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Comput. Methods Appl. Mech. Eng. 196, 1216–1243 (2007)CrossRefMATHMathSciNetGoogle Scholar
  64. J. Parmigiani, M.D. Thouless, The roles of toughness and cohesive strength on crack deflection at interfaces. J. Mech. Phys. Sol. 54, 266–287 (2006)CrossRefMATHGoogle Scholar
  65. J. Parmigiani, M.D. Thouless, The effects of cohesive strength and toughness on mixed-mode delamination of beam-like geometries. Eng. Fract. Mech. 74, 2675–2699 (2007)CrossRefGoogle Scholar
  66. S.T. Pinho, P. Robinson, L. Iannucci, Fracture toughness of the tensile and compressive fibre failure modes in laminated composites. Compos. Sci. Technol. 66, 2069–2079 (2006)CrossRefGoogle Scholar
  67. S. Ramanathan, D. Ertaz, D.S. Fisher, Quasistatic crack propagation in heterogeneous media. Phys. Rev. Lett. 79, 873–876 (1997)CrossRefGoogle Scholar
  68. J.N. Reddy, Multiscale computational model for predicting damage evolution in viscoelastic composites subjected to impact loading technical report to U.S. Army Research Office, 1-31 (2005)Google Scholar
  69. J.J.C. Remmers, R. de Borst, A. Needleman, A cohesive segments method for the simulation of crack growth. Comput. Mech. 31(1–2), 69–77 (2003)CrossRefMATHGoogle Scholar
  70. S. Rudraraju et al., In-plane fracture of laminated fiber reinforced composites with varying fracture resistance: experimental observations and numerical crack propagation simulations. Int. J. Sol. Struct. 47, 901–911 (2010)CrossRefMATHGoogle Scholar
  71. S. Rudraraju et al., Experimental observations and numerical simulations of curved crack propagation in laminated fiber composites. Compos. Sci. Technol. 72, 1064–1074 (2011)CrossRefGoogle Scholar
  72. K.W. Shahwan, A.M. Waas, Non-self-similar decohesion along a finite interface of unilaterally constrained delaminations. Proc. Roy. Soc. Lon. A 453, 515–550 (1997)CrossRefMathSciNetGoogle Scholar
  73. M.M. Shokrieh, L.B. Lessard, Progressive fatigue damage modeling of composite materials, Part I: Modeling. J. Compos. Mater. 34(13), 1056–1080 (2000)CrossRefGoogle Scholar
  74. S.J. Song, A.M. Waas, Energy-based mechanical model for mixed mode failure of laminated composites. AIAA J. 33, 739–745 (1995)CrossRefGoogle Scholar
  75. J.H. Song, P.M.A. Areias, T. Belytschko, A method for dynamic crack and shear band propagation with phantom nodes. Int. J. Numer. Meth. Eng. 67, 868–893 (2006)CrossRefMATHGoogle Scholar
  76. R. Talreja, Multiscale modeling in damage mechanics of composite materials. J. Mater. Sci. 41, 6800–6812 (2006)CrossRefGoogle Scholar
  77. X.D. Tang et al., Progressive failure analysis of 2x2 braided composites exhibiting multiscale heterogeneity. Compos. Sci. Technol. 66, 2580–2590 (2006)CrossRefGoogle Scholar
  78. T.-E. Tay, Characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001. Appl. Mech. Rev. 56(1), 1–32 (2003)CrossRefGoogle Scholar
  79. M.D. Thouless, Crack spacing in brittle films on elastic substrates. J. Am. Ceram. Soc. 73, 2144–2146 (1990)CrossRefGoogle Scholar
  80. M.D. Thouless, Q.D. Yang, A parametric study of the peel test. Int. J. Adhes. Adhes. 28, 176–184 (2008)CrossRefGoogle Scholar
  81. A. Turon et al., A damage model for the simulation of delamination in advanced composites under variable-mode loading. Mech. Mater. 38, 1072–1089 (2006)CrossRefGoogle Scholar
  82. A. Turon et al., An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Eng. Fract. Mech. 74, 1665–1682 (2007)CrossRefGoogle Scholar
  83. F.P. Van de Meer, L.J. Sluys, Continuum models for the analysis of progressive failure in composite laminates. J. Compos. Mater. 43, 2131–2156 (2009a)CrossRefGoogle Scholar
  84. F.P. Van de Meer, L.J. Sluys, A phantom node formulation with mixed mode cohesive law for splitting in laminates. Int. J. Fract. 158, 107–124 (2009b)CrossRefMATHGoogle Scholar
  85. F.P. Van de Meer, C. Oliver, L.J. Sluys, Computational analysis of progressive failure in a notched laminate including shear nonlinearity and fiber failure. Compos. Sci. Technol. 70, 692–700 (2010)CrossRefGoogle Scholar
  86. A.S.D. Wang, F.W. Crossman, Initiation and growth of transverse cracks and delaminations. J. Compos. Mater. 14, 71–87 (1980)CrossRefGoogle Scholar
  87. J.S. Wang, Z. Suo, Experimental determination of interfacial toughness using Brazil-nut-sandwich. Acta Metall. 38, 1279–1290 (1990)CrossRefGoogle Scholar
  88. M.R. Wisnom, The effect of fibre rotation in +/−45 degree tension tests on measured shear properties. Composites 26, 25–32 (1994)CrossRefGoogle Scholar
  89. M.R. Wisnom, F.-K. Chang, Modelling of splitting and delamination in notched cross-ply laminates. Compos. Sci. Technol. 60, 2849–2856 (2000)CrossRefGoogle Scholar
  90. M.R. Wisnom, M.I. Jones, Size effects in interlaminar tensile and shear strength of unidirectional glass fibre/epoxy. J. Reinf. Plast. Compos. 15, 2–15 (1996)Google Scholar
  91. D. Xie et al., Discrete cohesive zone model to simulate static fracture in 2D tri-axially braided carbon fiber composites. J. Compos. Mater. 40, 2025–2046 (2006)CrossRefGoogle Scholar
  92. Q.D. Yang, B.N. Cox, Cohesive zone models for damage evolution in laminated composites. Int. J. Fract. 133(2), 107–137 (2005)CrossRefMATHGoogle Scholar
  93. Q.D. Yang, M.D. Thouless, Mixed mode fracture of plastically-deforming adhesive joints. Int. J. Fract. 110, 175–187 (2001a)CrossRefGoogle Scholar
  94. Q. Yang, M.D. Thouless, Mixed mode fracture of plastically-deforming adhesive joints. Int. Fract. 110, 175–187 (2001b)CrossRefGoogle Scholar
  95. Q.D. Yang, M.D. Thouless, S.M. Ward, Numerical simulations of adhesively-bonded beams failing with extensive plastic deformation. J. Mech. Phys. Sol. 47, 1337–1353 (1999)CrossRefMATHGoogle Scholar
  96. Q.D. Yang, M.D. Thouless, S.M. Ward, Elastic–plastic mode-II fracture of adhesive joints. Int. J. Sol. Struct. 38, 3251–3262 (2001)CrossRefMATHGoogle Scholar
  97. Q.D. Yang et al., Fracture and length scales in human cortical bone: the necessity of nonlinear fracture models. Biomaterials 27, 2095–2113 (2006a)CrossRefGoogle Scholar
  98. Q.D. Yang et al., Re-evaluating the toughness of human cortical bone. Bone 38, 878–887 (2006b)CrossRefGoogle Scholar
  99. Q.D. Yang et al., An improved cohesive element for shell delamination analyses. Int. J. Numer. Meth. Eng. 83(5), 611–641 (2010)MATHGoogle Scholar
  100. Q.D. Yang et al., Virtual testing for advanced aerospace composites: advances and future needs. J. Eng. Mater. Technol. 133, 11002–11008 (2011)CrossRefGoogle Scholar
  101. Q.D. Yang, X. J. Fang, Revisiting crack kinking in cohesive materials. Unpublished results, 2013Google Scholar
  102. T. Ye, Z. Suo, A.G. Evans, Thin film cracking and the roles of substrate and interface. Int. J. Sol. Struct. 29, 2639–2648 (1992)CrossRefGoogle Scholar
  103. Z. Zhang, Z. Suo, Split singularities and the competition between crack penetration and debond at a bimaterial interface. Int. J. Struct. 44, 4559–4573 (2007)CrossRefMATHGoogle Scholar
  104. Z.Q. Zhou et al., The evolution of a transverse intra-ply crack coupled to delamination cracks. Int. J. Fract. 165, 77–92 (2010)CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of MiamiCoral GablesUSA

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